Unitary Friedberg--Jacquet periods and anticyclotomic p-adic L-functions

2024/03/09 by Graham, Andrew
#11F67 #11F77 #11G18 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2403.05960

Abstract

We extend the construction of the p-adic L-function interpolating unitary Friedberg--Jacquet periods in previous work of the author to include the p-adic variation of Maass--Shimura differential operators. In particular, we develop a theory of nearly overconvergent automorphic forms in higher degrees of coherent cohomology for unitary Shimura varieties generalising previous work for modular curves. The construction of this p-adic L-function can be viewed as a higher-dimensional generalisation of the work of Bertolini--Darmon--Prasanna and Castella--Hsieh, and the inclusion of this extra variable arising from the p-adic iteration of differential operators will play a key role in relating values of this p-adic L-function to p-adic regulators of special cycles on unitary Shimura varieties.

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